Heroic Strikes will get you two with a faction consumable ghost on for strikes most of the time. Even without it you still have a high chance to get two.
Crucible will usually generate one a match, sometimes two with a faction consumable. I personally think heroic strikes are faster, plus more loot but it's definitely not that hard of a grind.
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I did some heroics got bored then went to pvp. Maybe a little of both is also an option.
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You can also get zero for stretches as well.
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You can also get a blue one as well which is most satisfying.
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Not a lot luck there for me. My last 3 grinds were for 20, then 20, then 30. I finished the first 2 and I'm 15 out of 30 for the 3rd and haven't had a single blue drop. I get the occasional 2 greens to drop, but that's almost always followed or proceeded by not getting one at all so that kind of evens out.
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Absolutely.
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This is probably limited to when you are playing with peope/not getting matchmaked with incompetent players.